The invention is based on an apparatus for producing tubular-pouch packages as described in the specification. In an apparatus of this kind known in German Offenlegungsschrift No. 15 86 328, cooling air is blown onto the transverse seam, which closes the bottom of the tubular-pouch package, after the heat sealing chuck of the transverse-seam welding apparatus has been lifted away from the tube. The transverse seam thus hardens rapidly, so that there is little time for the product, which is introduced into the end of the tube while the heat sealing process is still going on, to force the still-soft sealed seam open. However, with thick packaging materials, a long period of time is required to draw off the heat, and it frequently happens that the bottom seam of a tubular-pouch package will burst open.